Abstract
We consider the Cauchy problem in $\mathbb {R}^N$, $N \geq 1$, for the semi-linear Schr\"odinger equation with fractional Laplacian. We present the local well-posedness of solutions in $H^{{\alpha }/{2}}(\mathbb {R}^N)$, $0\lt \alpha \lt 2$. We prove a finite-time blow-up result, under suitable conditions on the initial data.
Citation
A.Z. Fino. I. Dannawi. M. Kirane. "Blow-up of solutions for semilinear fractional Schrödinger equations." J. Integral Equations Applications 30 (1) 67 - 80, 2018. https://doi.org/10.1216/JIE-2018-30-1-67
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